diff --git a/src/HOL/Tools/Sledgehammer/sledgehammer_util.ML b/src/HOL/Tools/Sledgehammer/sledgehammer_util.ML
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_util.ML
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_util.ML
@@ -1,157 +1,157 @@
 (*  Title:      HOL/Tools/Sledgehammer/sledgehammer_util.ML
     Author:     Jasmin Blanchette, TU Muenchen
 
 General-purpose functions used by the Sledgehammer modules.
 *)
 
 signature SLEDGEHAMMER_UTIL =
 sig
   val sledgehammerN : string
   val log2 : real -> real
   val app_hd : ('a -> 'a) -> 'a list -> 'a list
   val plural_s : int -> string
   val serial_commas : string -> string list -> string list
   val simplify_spaces : string -> string
   val with_cleanup : ('a -> unit) -> ('a -> 'b) -> 'a -> 'b
   val parse_bool_option : bool -> string -> string -> bool option
   val parse_time : string -> string -> Time.time
   val subgoal_count : Proof.state -> int
   val thms_in_proof : int -> (string Symtab.table * string Symtab.table) option -> thm ->
     string list option
   val thms_of_name : Proof.context -> string -> thm list
   val one_day : Time.time
   val one_year : Time.time
   val hackish_string_of_term : Proof.context -> term -> string
   val spying : bool -> (unit -> Proof.state * int * string * string) -> unit
 end;
 
 structure Sledgehammer_Util : SLEDGEHAMMER_UTIL =
 struct
 
 open ATP_Util
 
 val sledgehammerN = "sledgehammer"
 
 val log10_2 = Math.log10 2.0
 fun log2 n = Math.log10 n / log10_2
 
 fun app_hd f (x :: xs) = f x :: xs
 
 fun plural_s n = if n = 1 then "" else "s"
 
 val serial_commas = Try.serial_commas
 val simplify_spaces = strip_spaces false (K true)
 
 fun with_cleanup clean_up f x =
   Exn.capture f x
   |> tap (fn _ => clean_up x)
   |> Exn.release
 
 fun parse_bool_option option name s =
   (case s of
      "smart" => if option then NONE else raise Option.Option
    | "false" => SOME false
    | "true" => SOME true
    | "" => SOME true
    | _ => raise Option.Option)
   handle Option.Option =>
     let val ss = map quote ((option ? cons "smart") ["true", "false"]) in
       error ("Parameter " ^ quote name ^ " must be assigned " ^
        space_implode " " (serial_commas "or" ss))
     end
 
 val has_junk =
   exists (fn s => not (Symbol.is_digit s) andalso s <> ".") o raw_explode (* FIXME Symbol.explode (?) *)
 
 fun parse_time name s =
   let val secs = if has_junk s then NONE else Real.fromString s in
     if is_none secs orelse the secs < 0.0 then
       error ("Parameter " ^ quote name ^ " must be assigned a nonnegative number of seconds \
         \(e.g., \"60\", \"0.5\") or \"none\"")
     else
       seconds (the secs)
   end
 
-val subgoal_count = Try.subgoal_count
+val subgoal_count = Logic.count_prems o Thm.prop_of o #goal o Proof.goal;
 
 exception TOO_MANY of unit
 
 (* FIXME: Similar yet different code in "mirabelle.ML". The code here has a few fixes that seem to
    be missing over there; or maybe the two code portions are not doing the same? *)
 fun fold_body_thm max_thms outer_name (map_plain_name, map_inclass_name) body =
   let
     fun app_thm map_name (_, thm_node) (accum as (num_thms, names)) =
       let
         val name = Proofterm.thm_node_name thm_node
         val body = Proofterm.thm_node_body thm_node
         val (anonymous, enter_class) =
           (* The "name = outer_name" case caters for the uncommon case where the proved theorem
              occurs in its own proof (e.g., "Transitive_Closure.trancl_into_trancl"). *)
           if name = "" orelse name = outer_name then (true, false)
           else if map_inclass_name name = SOME outer_name then (true, true)
           else (false, false)
       in
         if anonymous then
           (case Future.peek body of
             SOME (Exn.Res the_body) =>
             app_body (if enter_class then map_inclass_name else map_name) the_body accum
           | NONE => accum)
         else
           (case map_name name of
             SOME name' =>
             if member (op =) names name' then accum
             else if num_thms = max_thms then raise TOO_MANY ()
             else (num_thms + 1, name' :: names)
           | NONE => accum)
       end
     and app_body map_name (PBody {thms, ...}) = fold (app_thm map_name) thms
   in
     snd (app_body map_plain_name body (0, []))
   end
 
 fun thms_in_proof max_thms name_tabs th =
   (case try Thm.proof_body_of th of
     NONE => NONE
   | SOME body =>
     let val map_names = (case name_tabs of SOME p => apply2 Symtab.lookup p | NONE => `I SOME) in
       SOME (fold_body_thm max_thms (Thm.get_name_hint th) map_names (Proofterm.strip_thm_body body))
       handle TOO_MANY () => NONE
     end)
 
 fun thms_of_name ctxt name =
   let
     val get = maps (Proof_Context.get_fact ctxt o fst)
     val keywords = Thy_Header.get_keywords' ctxt
   in
     Symbol_Pos.explode (name, Position.start)
     |> Token.tokenize keywords {strict = false}
     |> filter Token.is_proper
     |> Source.of_list
     |> Source.source Token.stopper (Parse.thms1 >> get)
     |> Source.exhaust
   end
 
 val one_day = seconds (24.0 * 60.0 * 60.0)
 val one_year = seconds (365.0 * 24.0 * 60.0 * 60.0)
 
 fun hackish_string_of_term ctxt =
   (* FIXME: map_aterms (fn Free (s, T) => Free (if Name.is_internal s then "_" else s, T) | t => t)
   #> *) Print_Mode.setmp [] (Syntax.string_of_term ctxt)
   #> YXML.content_of
   #> simplify_spaces
 
 val spying_version = "d"
 
 fun spying false _ = ()
   | spying true f =
     let
       val (state, i, tool, message) = f ()
       val ctxt = Proof.context_of state
       val goal = Logic.get_goal (Thm.prop_of (#goal (Proof.goal state))) i
       val hash = String.substring (SHA1.rep (SHA1.digest (hackish_string_of_term ctxt goal)), 0, 12)
     in
       File.append (Path.explode "$ISABELLE_HOME_USER/spy_sledgehammer")
         (spying_version ^ " " ^ timestamp () ^ ": " ^ hash ^ ": " ^ tool ^ ": " ^ message ^ "\n")
     end
 
 end;
diff --git a/src/Pure/Isar/proof.ML b/src/Pure/Isar/proof.ML
--- a/src/Pure/Isar/proof.ML
+++ b/src/Pure/Isar/proof.ML
@@ -1,1344 +1,1347 @@
 (*  Title:      Pure/Isar/proof.ML
     Author:     Markus Wenzel, TU Muenchen
 
 The Isar/VM proof language interpreter: maintains a structured flow of
 context elements, goals, refinements, and facts.
 *)
 
 signature PROOF =
 sig
   type context = Proof.context
   type method = Method.method
   type state
   val init: context -> state
   val level: state -> int
   val assert_bottom: bool -> state -> state
   val context_of: state -> context
   val theory_of: state -> theory
   val map_context: (context -> context) -> state -> state
   val map_context_result : (context -> 'a * context) -> state -> 'a * state
   val map_contexts: (context -> context) -> state -> state
   val propagate_ml_env: state -> state
   val report_improper: state -> unit
   val the_facts: state -> thm list
   val the_fact: state -> thm
   val set_facts: thm list -> state -> state
   val reset_facts: state -> state
   val improper_reset_facts: state -> state
   val assert_forward: state -> state
   val assert_chain: state -> state
   val assert_forward_or_chain: state -> state
   val assert_backward: state -> state
   val assert_no_chain: state -> state
   val enter_forward: state -> state
   val enter_chain: state -> state
   val enter_backward: state -> state
   val using_facts: thm list -> state -> state
   val pretty_state: state -> Pretty.T list
   val refine: Method.text -> state -> state Seq.result Seq.seq
   val refine_end: Method.text -> state -> state Seq.result Seq.seq
   val refine_singleton: Method.text -> state -> state
   val refine_insert: thm list -> state -> state
   val refine_primitive: (Proof.context -> thm -> thm) -> state -> state
+  val goal_finished: state -> bool
   val raw_goal: state -> {context: context, facts: thm list, goal: thm}
   val goal: state -> {context: context, facts: thm list, goal: thm}
   val simple_goal: state -> {context: context, goal: thm}
   val let_bind: (term list * term) list -> state -> state
   val let_bind_cmd: (string list * string) list -> state -> state
   val write: Syntax.mode -> (term * mixfix) list -> state -> state
   val write_cmd: Syntax.mode -> (string * mixfix) list -> state -> state
   val fix: (binding * typ option * mixfix) list -> state -> state
   val fix_cmd: (binding * string option * mixfix) list -> state -> state
   val assm: Assumption.export -> (binding * typ option * mixfix) list ->
     (term * term list) list list -> (Thm.binding * (term * term list) list) list ->
     state -> state
   val assm_cmd: Assumption.export -> (binding * string option * mixfix) list ->
     (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
     state -> state
   val assume: (binding * typ option * mixfix) list ->
     (term * term list) list list -> (Thm.binding * (term * term list) list) list ->
     state -> state
   val assume_cmd: (binding * string option * mixfix) list ->
     (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
     state -> state
   val presume: (binding * typ option * mixfix) list ->
     (term * term list) list list -> (Thm.binding * (term * term list) list) list ->
     state -> state
   val presume_cmd: (binding * string option * mixfix) list ->
     (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
     state -> state
   val chain: state -> state
   val chain_facts: thm list -> state -> state
   val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state
   val note_thmss_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
   val from_thmss: ((thm list * attribute list) list) list -> state -> state
   val from_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
   val with_thmss: ((thm list * attribute list) list) list -> state -> state
   val with_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
   val supply: (Thm.binding * (thm list * attribute list) list) list -> state -> state
   val supply_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
   val using: ((thm list * attribute list) list) list -> state -> state
   val using_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
   val unfolding: ((thm list * attribute list) list) list -> state -> state
   val unfolding_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
   val case_: Thm.binding * ((string * Position.T) * binding option list) -> state -> state
   val case_cmd: Attrib.binding * ((string * Position.T) * binding option list) -> state -> state
   val define: (binding * typ option * mixfix) list ->
     (binding * typ option * mixfix) list ->
     (Thm.binding * (term * term list) list) list -> state -> state
   val define_cmd: (binding * string option * mixfix) list ->
     (binding * string option * mixfix) list ->
     (Attrib.binding * (string * string list) list) list -> state -> state
   val begin_block: state -> state
   val next_block: state -> state
   val end_block: state -> state
   val begin_notepad: context -> state
   val end_notepad: state -> context
   val is_notepad: state -> bool
   val reset_notepad: state -> state
   val proof: Method.text_range option -> state -> state Seq.result Seq.seq
   val defer: int -> state -> state
   val prefer: int -> state -> state
   val apply: Method.text_range -> state -> state Seq.result Seq.seq
   val apply_end: Method.text_range -> state -> state Seq.result Seq.seq
   val local_qed: Method.text_range option * bool -> state -> state
   val theorem: Method.text option -> (thm list list -> context -> context) ->
     (term * term list) list list -> context -> state
   val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->
     (string * string list) list list -> context -> state
   val global_qed: Method.text_range option * bool -> state -> context
   val schematic_goal: state -> bool
   val is_relevant: state -> bool
   val local_terminal_proof: Method.text_range * Method.text_range option -> state -> state
   val local_default_proof: state -> state
   val local_immediate_proof: state -> state
   val local_skip_proof: bool -> state -> state
   val local_done_proof: state -> state
   val global_terminal_proof: Method.text_range * Method.text_range option -> state -> context
   val global_default_proof: state -> context
   val global_immediate_proof: state -> context
   val global_skip_proof: bool -> state -> context
   val global_done_proof: state -> context
   val internal_goal: (context -> (string * string) * (string * thm list) list -> unit) ->
     Proof_Context.mode -> bool -> string -> Method.text option ->
     (context * thm list list -> state -> state) ->
     (binding * typ option * mixfix) list ->
     (Thm.binding * (term * term list) list) list ->
     (Thm.binding * (term * term list) list) list -> state -> thm list * state
   val have: bool -> Method.text option -> (context * thm list list -> state -> state) ->
     (binding * typ option * mixfix) list ->
     (Thm.binding * (term * term list) list) list ->
     (Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
   val have_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
     (binding * string option * mixfix) list ->
     (Attrib.binding * (string * string list) list) list ->
     (Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
   val show: bool -> Method.text option -> (context * thm list list -> state -> state) ->
     (binding * typ option * mixfix) list ->
     (Thm.binding * (term * term list) list) list ->
     (Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
   val show_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
     (binding * string option * mixfix) list ->
     (Attrib.binding * (string * string list) list) list ->
     (Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
   val future_proof: (state -> ('a * context) future) -> state -> 'a future * state
   val local_future_terminal_proof: Method.text_range * Method.text_range option -> state -> state
   val global_future_terminal_proof: Method.text_range * Method.text_range option -> state -> context
 end;
 
 structure Proof: PROOF =
 struct
 
 type context = Proof.context;
 type method = Method.method;
 
 
 (** proof state **)
 
 (* datatype state *)
 
 datatype mode = Forward | Chain | Backward;
 
 datatype state =
   State of node Stack.T
 and node =
   Node of
    {context: context,
     facts: (thm list * bool) option,
     mode: mode,
     goal: goal option}
 and goal =
   Goal of
    {statement: (string * Position.T) * term list list * term,
       (*goal kind and statement (starting with vars), initial proposition*)
     using: thm list,                      (*goal facts*)
     goal: thm,                            (*subgoals \<Longrightarrow> statement*)
     before_qed: Method.text option,
     after_qed:
       (context * thm list list -> state -> state) *
       (context * thm list list -> context -> context)};
 
 val _ =
   ML_system_pp (fn _ => fn _ => fn _: state =>
     Pretty.to_polyml (Pretty.str "<Proof.state>"));
 
 fun make_goal (statement, using, goal, before_qed, after_qed) =
   Goal {statement = statement, using = using, goal = goal,
     before_qed = before_qed, after_qed = after_qed};
 
 fun make_node (context, facts, mode, goal) =
   Node {context = context, facts = facts, mode = mode, goal = goal};
 
 fun map_node f (Node {context, facts, mode, goal}) =
   make_node (f (context, facts, mode, goal));
 
 val init_context =
   Proof_Context.set_stmt true #>
   Proof_Context.map_naming (K Name_Space.local_naming);
 
 fun init ctxt =
   State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
 
 fun top (State stack) = Stack.top stack |> (fn Node node => node);
 fun map_top f (State stack) = State (Stack.map_top (map_node f) stack);
 fun map_all f (State stack) = State (Stack.map_all (map_node f) stack);
 
 
 
 (** basic proof state operations **)
 
 (* block structure *)
 
 fun open_block (State stack) = State (Stack.push stack);
 
 fun close_block (State stack) = State (Stack.pop stack)
   handle List.Empty => error "Unbalanced block parentheses";
 
 fun level (State stack) = Stack.level stack;
 
 fun assert_bottom b state =
   let val b' = level state <= 2 in
     if b andalso not b' then error "Not at bottom of proof"
     else if not b andalso b' then error "Already at bottom of proof"
     else state
   end;
 
 
 (* context *)
 
 val context_of = #context o top;
 val theory_of = Proof_Context.theory_of o context_of;
 
 fun map_context f =
   map_top (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
 
 fun map_context_result f state =
   f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
 
 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
 
 fun propagate_ml_env state = map_contexts
   (Context.proof_map (ML_Env.inherit [Context.Proof (context_of state)])) state;
 
 
 (* facts *)
 
 fun report_improper state =
   Context_Position.report (context_of state) (Position.thread_data ()) Markup.improper;
 
 val get_facts = #facts o top;
 
 fun the_facts state =
   (case get_facts state of
     SOME (facts, proper) => (if proper then () else report_improper state; facts)
   | NONE => error "No current facts available");
 
 fun the_fact state =
   (case the_facts state of
     [thm] => thm
   | _ => error "Single theorem expected");
 
 fun put_facts index facts =
   map_top (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
   map_context (Proof_Context.put_thms index (Auto_Bind.thisN, Option.map #1 facts));
 
 fun set_facts thms = put_facts false (SOME (thms, true));
 val reset_facts = put_facts false NONE;
 
 fun improper_reset_facts state =
   (case get_facts state of
     SOME (thms, _) => put_facts false (SOME (thms, false)) state
   | NONE => state);
 
 fun these_factss more_facts (named_factss, state) =
   (named_factss, state |> set_facts (maps snd named_factss @ more_facts));
 
 fun export_facts inner outer =
   (case get_facts inner of
     NONE => reset_facts outer
   | SOME (thms, proper) =>
       let val thms' = Proof_Context.export (context_of inner) (context_of outer) thms
       in put_facts true (SOME (thms', proper)) outer end);
 
 
 (* mode *)
 
 val get_mode = #mode o top;
 fun put_mode mode = map_top (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
 
 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
 
 fun assert_mode pred state =
   let val mode = get_mode state in
     if pred mode then state
     else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
   end;
 
 val assert_forward = assert_mode (fn mode => mode = Forward);
 val assert_chain = assert_mode (fn mode => mode = Chain);
 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
 val assert_backward = assert_mode (fn mode => mode = Backward);
 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
 
 val enter_forward = put_mode Forward;
 val enter_chain = put_mode Chain;
 val enter_backward = put_mode Backward;
 
 
 (* current goal *)
 
 fun current_goal state =
   (case top state of
     {context = ctxt, goal = SOME (Goal goal), ...} => (ctxt, goal)
   | _ => error "No current goal");
 
 fun assert_current_goal g state =
   let val g' = can current_goal state in
     if g andalso not g' then error "No goal in this block"
     else if not g andalso g' then error "Goal present in this block"
     else state
   end;
 
 fun put_goal goal = map_top (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));
 
 val set_goal = put_goal o SOME;
 val reset_goal = put_goal NONE;
 
 val before_qed = #before_qed o #2 o current_goal;
 
 
 (* nested goal *)
 
 fun map_goal f (State stack) =
   (case Stack.dest stack of
     (Node {context = ctxt, facts, mode, goal = SOME goal}, node :: nodes) =>
       let
         val Goal {statement, using, goal, before_qed, after_qed} = goal;
         val (ctxt', statement', using', goal', before_qed', after_qed') =
           f (ctxt, statement, using, goal, before_qed, after_qed);
         val goal' = make_goal (statement', using', goal', before_qed', after_qed');
       in State (Stack.make (make_node (ctxt', facts, mode, SOME goal')) (node :: nodes)) end
   | (top_node, node :: nodes) =>
       let
         val State stack' = map_goal f (State (Stack.make node nodes));
         val (node', nodes') = Stack.dest stack';
       in State (Stack.make top_node (node' :: nodes')) end
   | _ => State stack);
 
 fun provide_goal goal =
   map_goal (fn (ctxt, statement, using, _, before_qed, after_qed) =>
     (ctxt, statement, using, goal, before_qed, after_qed));
 
 fun using_facts using =
   map_goal (fn (ctxt, statement, _, goal, before_qed, after_qed) =>
     (ctxt, statement, using, goal, before_qed, after_qed));
 
 fun find_goal state =
   (case try current_goal state of
     SOME ctxt_goal => ctxt_goal
   | NONE => find_goal (close_block state handle ERROR _ => error "No proof goal"));
 
 fun get_goal state =
   let val (ctxt, {using, goal, ...}) = find_goal state
   in (ctxt, (using, goal)) end;
 
 
 
 (** pretty_state **)
 
 local
 
 fun pretty_facts _ _ NONE = []
   | pretty_facts ctxt s (SOME ths) = [Proof_Display.pretty_goal_facts ctxt s ths];
 
 fun pretty_sep prts [] = prts
   | pretty_sep [] prts = prts
   | pretty_sep prts1 prts2 = prts1 @ [Pretty.str ""] @ prts2;
 
 in
 
 fun pretty_state state =
   let
     val {context = ctxt, facts, mode, goal = _} = top state;
     val verbose = Config.get ctxt Proof_Context.verbose;
 
     fun prt_goal (SOME (_, {statement = _, using, goal, before_qed = _, after_qed = _})) =
           pretty_sep
             (pretty_facts ctxt "using"
               (if mode <> Backward orelse null using then NONE else SOME using))
             ([Proof_Display.pretty_goal_header goal] @ Goal_Display.pretty_goals ctxt goal)
       | prt_goal NONE = [];
 
     val prt_ctxt =
       if verbose orelse mode = Forward then Proof_Context.pretty_context ctxt
       else if mode = Backward then Proof_Context.pretty_ctxt ctxt
       else [];
 
     val position_markup = Position.markup (Position.thread_data ()) Markup.position;
   in
     [Pretty.block
       [Pretty.mark_str (position_markup, "proof"), Pretty.str (" (" ^ mode_name mode ^ ")")]] @
     (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
     (if verbose orelse mode = Forward then
        pretty_sep (pretty_facts ctxt "" (Option.map #1 facts)) (prt_goal (try find_goal state))
      else if mode = Chain then pretty_facts ctxt "picking" (Option.map #1 facts)
      else prt_goal (try find_goal state))
   end;
 
 end;
 
 
 
 (** proof steps **)
 
 (* refine via method *)
 
 local
 
 fun apply_method text ctxt state =
   find_goal state |> (fn (goal_ctxt, {statement, using, goal, before_qed, after_qed}) =>
     Method.evaluate text ctxt using (goal_ctxt, goal)
     |> Seq.map_result (fn (goal_ctxt', goal') =>
         state |> map_goal (K (goal_ctxt', statement, using, goal', before_qed, after_qed))));
 
 in
 
 fun refine text state = apply_method text (context_of state) state;
 fun refine_end text state = apply_method text (#1 (find_goal state)) state;
 
 fun refine_singleton text = refine text #> Seq.the_result "";
 
 fun refine_insert ths =
   refine_singleton (Method.Basic (K (Method.insert ths)));
 
 fun refine_primitive r =
   refine_singleton (Method.Basic (fn ctxt => fn _ => CONTEXT_TACTIC (PRIMITIVE (r ctxt))));
 
 end;
 
 
 (* refine via sub-proof *)
 
 local
 
 fun finish_tac _ 0 = K all_tac
   | finish_tac ctxt n =
       Goal.norm_hhf_tac ctxt THEN'
       SUBGOAL (fn (goal, i) =>
         if can Logic.unprotect (Logic.strip_assums_concl goal) then
           eresolve_tac ctxt [Drule.protectI] i THEN finish_tac ctxt (n - 1) i
         else finish_tac ctxt (n - 1) (i + 1));
 
 fun goal_tac ctxt rule =
   Goal.norm_hhf_tac ctxt THEN'
   resolve_tac ctxt [rule] THEN'
   finish_tac ctxt (Thm.nprems_of rule);
 
 fun FINDGOAL tac st =
   let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)
   in find 1 (Thm.nprems_of st) st end;
 
 fun protect_prem i th =
   Thm.bicompose NONE {flatten = false, match = false, incremented = true}
     (false, Drule.incr_indexes th Drule.protectD, 1) i th
   |> Seq.hd;
 
 fun protect_prems th =
   fold_rev protect_prem (1 upto Thm.nprems_of th) th;
 
 in
 
 fun refine_goals print_rule result_ctxt result state =
   let
     val (goal_ctxt, (_, goal)) = get_goal state;
     fun refine rule st =
       (print_rule goal_ctxt rule; FINDGOAL (goal_tac goal_ctxt rule) st);
   in
     result
     |> map (Raw_Simplifier.norm_hhf result_ctxt #> protect_prems)
     |> Proof_Context.goal_export result_ctxt goal_ctxt
     |> (fn rules => Seq.lift provide_goal (EVERY (map refine rules) goal) state)
   end;
 
 end;
 
 
 (* conclude goal *)
 
 fun conclude_goal ctxt goal propss =
   let
     val thy = Proof_Context.theory_of ctxt;
 
     val _ =
       Context.subthy_id (Thm.theory_id goal, Context.theory_id thy) orelse
         error "Bad background theory of goal state";
     val _ = Thm.no_prems goal orelse error (Proof_Display.string_of_goal ctxt goal);
 
     fun err_lost () = error ("Lost goal structure:\n" ^ Thm.string_of_thm ctxt goal);
 
     val th =
       (Goal.conclude (Thm.close_derivation \<^here> goal) handle THM _ => err_lost ())
       |> Drule.flexflex_unique (SOME ctxt)
       |> Thm.check_shyps ctxt
       |> Thm.check_hyps (Context.Proof ctxt);
 
     val goal_propss = filter_out null propss;
     val results =
       Conjunction.elim_balanced (length goal_propss) th
       |> map2 Conjunction.elim_balanced (map length goal_propss)
       handle THM _ => err_lost ();
     val _ =
       Unify.matches_list (Context.Proof ctxt)
         (map (Soft_Type_System.purge ctxt) (flat goal_propss)) (map Thm.prop_of (flat results))
         orelse error ("Proved a different theorem:\n" ^ Thm.string_of_thm ctxt th);
 
     fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
       | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
       | recover_result [] [] = []
       | recover_result _ _ = err_lost ();
   in recover_result propss results end;
 
 val finished_goal_error = "Failed to finish proof";
 
 fun finished_goal pos state =
   let val (ctxt, (_, goal)) = get_goal state in
     if Thm.no_prems goal then Seq.Result state
     else
       Seq.Error (fn () =>
         finished_goal_error ^ Position.here pos ^ ":\n" ^
           Proof_Display.string_of_goal ctxt goal)
   end;
 
 
 (* goal views -- corresponding to methods *)
 
+val goal_finished = Thm.no_prems o #goal o #2 o find_goal;
+
 fun raw_goal state =
   let val (ctxt, (using, goal)) = get_goal state
   in {context = ctxt, facts = using, goal = goal} end;
 
 val goal = raw_goal o refine_insert [];
 
 fun simple_goal state =
   let
     val (_, (using, _)) = get_goal state;
     val (ctxt, (_, goal)) = get_goal (refine_insert using state);
   in {context = ctxt, goal = goal} end;
 
 fun method_error kind pos state =
   Seq.single (Proof_Display.method_error kind pos (raw_goal state));
 
 
 
 (*** structured proof commands ***)
 
 (** context elements **)
 
 (* let bindings *)
 
 local
 
 fun gen_bind prep_terms raw_binds =
   assert_forward #> map_context (fn ctxt =>
     let
       fun prep_bind (raw_pats, t) ctxt1 =
         let
           val T = Term.fastype_of t;
           val ctxt2 = Variable.declare_term t ctxt1;
           val pats = prep_terms (Proof_Context.set_mode Proof_Context.mode_pattern ctxt2) T raw_pats;
           val binds = Proof_Context.simult_matches ctxt2 (t, pats);
         in (binds, ctxt2) end;
 
       val ts = prep_terms ctxt dummyT (map snd raw_binds);
       val (binds, ctxt') = apfst flat (fold_map prep_bind (map fst raw_binds ~~ ts) ctxt);
       val binds' = map #1 binds ~~ Variable.exportT_terms ctxt' ctxt (map #2 binds);
 
       val ctxt'' =
         ctxt
         |> fold Variable.declare_term (map #2 binds')
         |> fold Proof_Context.bind_term binds';
       val _ = Variable.warn_extra_tfrees ctxt ctxt'';
     in ctxt'' end)
   #> reset_facts;
 
 fun read_terms ctxt T =
   map (Syntax.parse_term ctxt #> Type.constraint T) #> Syntax.check_terms ctxt;
 
 in
 
 val let_bind = gen_bind (fn ctxt => fn _ => map (Proof_Context.cert_term ctxt));
 val let_bind_cmd = gen_bind read_terms;
 
 end;
 
 
 (* concrete syntax *)
 
 local
 
 fun read_arg (c, mx) ctxt =
   (case Proof_Context.read_const {proper = false, strict = false} ctxt c of
     Free (x, _) =>
       let
         val ctxt' =
           ctxt |> is_none (Variable.default_type ctxt x) ?
             Variable.declare_constraints (Free (x, Mixfix.default_constraint mx));
         val t = Free (#1 (Proof_Context.inferred_param x ctxt'));
       in ((t, mx), ctxt') end
   | t => ((t, mx), ctxt));
 
 fun gen_write prep_arg mode args =
   assert_forward
   #> map_context (fold_map prep_arg args #-> Proof_Context.notation true mode)
   #> reset_facts;
 
 in
 
 val write = gen_write pair;
 val write_cmd = gen_write read_arg;
 
 end;
 
 
 (* fix *)
 
 local
 
 fun gen_fix add_fixes raw_fixes =
   assert_forward
   #> map_context (snd o add_fixes raw_fixes)
   #> reset_facts;
 
 in
 
 val fix = gen_fix Proof_Context.add_fixes;
 val fix_cmd = gen_fix Proof_Context.add_fixes_cmd;
 
 end;
 
 
 (* assume *)
 
 local
 
 fun gen_assume prep_statement prep_att export raw_fixes raw_prems raw_concls state =
   let
     val ctxt = context_of state;
 
     val bindings = map (apsnd (map (prep_att ctxt)) o fst) raw_concls;
     val {fixes = params, assumes = prems_propss, shows = concl_propss, result_binds, text, ...} =
       #1 (prep_statement raw_fixes raw_prems (map snd raw_concls) ctxt);
     val propss = (map o map) (Logic.close_prop params (flat prems_propss)) concl_propss;
   in
     state
     |> assert_forward
     |> map_context_result (fn ctxt =>
       ctxt
       |> Proof_Context.augment text
       |> fold Variable.maybe_bind_term result_binds
       |> fold_burrow (Assumption.add_assms export o map (Thm.cterm_of ctxt)) propss
       |-> (fn premss =>
         Proof_Context.note_thmss "" (bindings ~~ (map o map) (fn th => ([th], [])) premss)))
     |> these_factss [] |> #2
   end;
 
 in
 
 val assm = gen_assume Proof_Context.cert_statement (K I);
 val assm_cmd = gen_assume Proof_Context.read_statement Attrib.attribute_cmd;
 
 val assume = assm Assumption.assume_export;
 val assume_cmd = assm_cmd Assumption.assume_export;
 
 val presume = assm Assumption.presume_export;
 val presume_cmd = assm_cmd Assumption.presume_export;
 
 end;
 
 
 
 (** facts **)
 
 (* chain *)
 
 val chain =
   assert_forward
   #> (fn state => set_facts (Method.clean_facts (the_facts state)) state)
   #> enter_chain;
 
 fun chain_facts facts =
   set_facts facts
   #> chain;
 
 
 (* note etc. *)
 
 fun empty_bindings args = map (pair Binding.empty_atts) args;
 
 local
 
 fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
   state
   |> assert_forward
   |> map_context_result (fn ctxt => ctxt |> Proof_Context.note_thmss ""
     (Attrib.map_facts_refs (map (prep_atts ctxt)) (prep_fact ctxt) args))
   |> these_factss (more_facts state)
   ||> opt_chain
   |> opt_result;
 
 in
 
 val note_thmss = gen_thmss (K []) I #2 (K I) (K I);
 val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute_cmd Proof_Context.get_fact;
 
 val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o empty_bindings;
 val from_thmss_cmd =
   gen_thmss (K []) chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;
 
 val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o empty_bindings;
 val with_thmss_cmd =
   gen_thmss the_facts chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;
 
 val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
 
 end;
 
 
 (* facts during goal refinement *)
 
 local
 
 fun gen_supply prep_att prep_fact args state =
   state
   |> assert_backward
   |> map_context (fn ctxt => ctxt |> Proof_Context.note_thmss ""
        (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) args) |> snd);
 
 in
 
 val supply = gen_supply (K I) (K I);
 val supply_cmd = gen_supply Attrib.attribute_cmd Proof_Context.get_fact;
 
 end;
 
 
 (* using/unfolding *)
 
 local
 
 fun gen_using f g prep_att prep_fact args state =
   state
   |> assert_backward
   |> map_context_result
     (fn ctxt => ctxt |> Proof_Context.note_thmss ""
       (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) (empty_bindings args)))
   |> (fn (named_facts, state') =>
     state' |> map_goal (fn (goal_ctxt, statement, using, goal, before_qed, after_qed) =>
       let
         val ctxt = context_of state';
         val ths = maps snd named_facts;
       in (goal_ctxt, statement, f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
 
 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
 fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);
 val unfold_goals = Local_Defs.unfold_goals;
 
 in
 
 val using = gen_using append_using (K (K I)) (K I) (K I);
 val using_cmd = gen_using append_using (K (K I)) Attrib.attribute_cmd Proof_Context.get_fact;
 val unfolding = gen_using unfold_using unfold_goals (K I) (K I);
 val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute_cmd Proof_Context.get_fact;
 
 end;
 
 
 (* case *)
 
 local
 
 fun gen_case internal prep_att ((raw_binding, raw_atts), ((name, pos), xs)) state =
   let
     val ctxt = context_of state;
 
     val binding = if Binding.is_empty raw_binding then Binding.make (name, pos) else raw_binding;
     val atts = map (prep_att ctxt) raw_atts;
 
     val (asms, state') = state |> map_context_result (fn ctxt =>
       ctxt |> Proof_Context.apply_case (Proof_Context.check_case ctxt internal (name, pos) xs));
     val assumptions =
       asms |> map (fn (a, ts) => ((Binding.qualify_name true binding a, []), map (rpair []) ts));
   in
     state'
     |> assume [] [] assumptions
     |> map_context (fold Variable.unbind_term Auto_Bind.no_facts)
     |> `the_facts |-> (fn thms => note_thmss [((binding, atts), [(thms, [])])])
   end;
 
 in
 
 val case_ = gen_case true (K I);
 val case_cmd = gen_case false Attrib.attribute_cmd;
 
 end;
 
 
 (* define *)
 
 local
 
 fun gen_define prep_stmt prep_att raw_decls raw_fixes raw_defs state =
   let
     val _ = assert_forward state;
     val ctxt = context_of state;
 
     (*vars*)
     val ({vars, propss, result_binds, ...}, vars_ctxt) =
       prep_stmt (raw_decls @ raw_fixes) (map snd raw_defs) ctxt;
     val (decls, fixes) = chop (length raw_decls) vars;
     val show_term = Syntax.string_of_term vars_ctxt;
 
     (*defs*)
     fun match_defs (((b, _, mx), (_, Free (x, T))) :: more_decls) ((((y, U), t), _) :: more_defs) =
           if x = y then ((b, mx), (Binding.empty_atts, t)) :: match_defs more_decls more_defs
           else
             error ("Mismatch of declaration " ^ show_term (Free (x, T)) ^ " wrt. definition " ^
               show_term (Free (y, U)))
       | match_defs [] [] = []
       | match_defs more_decls more_defs =
           error ("Mismatch of declarations " ^ commas (map (show_term o #2 o #2) more_decls) ^
             (if null more_decls then "" else " ") ^
             "wrt. definitions " ^ commas (map (show_term o Free o #1 o #1) more_defs));
 
     val derived_def = Local_Defs.derived_def ctxt (K  []) {conditional = false};
     val defs1 = map (derived_def o Logic.close_prop (map #2 fixes) []) (flat propss);
     val defs2 = match_defs decls defs1;
     val (defs3, defs_ctxt) = Local_Defs.define defs2 ctxt;
 
     (*notes*)
     val def_thmss =
       map (fn (((_, prove), ((b, _), _)), (_, (_, th))) => (b, prove defs_ctxt th))
         (defs1 ~~ defs2 ~~ defs3)
       |> unflat (map snd raw_defs);
     val notes =
       map2 (fn ((a, raw_atts), _) => fn def_thms =>
         ((Thm.def_binding_optional (Binding.conglomerate (map #1 def_thms)) a,
           map (prep_att defs_ctxt) raw_atts), map (fn (_, th) => ([th], [])) def_thms))
         raw_defs def_thmss;
   in
     state
     |> map_context (K defs_ctxt #> fold Variable.bind_term result_binds)
     |> note_thmss notes
   end;
 
 in
 
 val define = gen_define Proof_Context.cert_stmt (K I);
 val define_cmd = gen_define Proof_Context.read_stmt Attrib.attribute_cmd;
 
 end;
 
 
 
 (** proof structure **)
 
 (* blocks *)
 
 val begin_block =
   assert_forward
   #> open_block
   #> reset_goal
   #> open_block;
 
 val next_block =
   assert_forward
   #> close_block
   #> open_block
   #> reset_goal
   #> reset_facts;
 
 fun end_block state =
   state
   |> assert_forward
   |> assert_bottom false
   |> close_block
   |> assert_current_goal false
   |> close_block
   |> export_facts state;
 
 
 (* global notepad *)
 
 val begin_notepad =
   init
   #> open_block
   #> map_context (Variable.set_body true)
   #> open_block;
 
 val end_notepad =
   assert_forward
   #> assert_bottom true
   #> close_block
   #> assert_current_goal false
   #> close_block
   #> context_of;
 
 fun get_notepad_context (State stack) =
   let
     fun escape [Node {goal = SOME _, ...}, Node {goal = NONE, ...}] = NONE
       | escape [Node {goal = SOME _, ...}] = NONE
       | escape [Node {goal = NONE, context = ctxt, ...}] = SOME ctxt
       | escape [] = NONE
       | escape (_ :: rest) = escape rest;
   in escape (op :: (Stack.dest stack)) end;
 
 val is_notepad = is_some o get_notepad_context;
 
 fun reset_notepad state =
   begin_notepad (the_default (context_of state) (get_notepad_context state));
 
 
 (* sub-proofs *)
 
 fun proof opt_text =
   Seq.APPEND
     (assert_backward
       #> refine (the_default Method.standard_text (Method.text opt_text))
       #> Seq.map_result
         (using_facts []
           #> enter_forward
           #> open_block
           #> reset_goal),
      method_error "initial" (Method.position opt_text));
 
 fun end_proof bot (prev_pos, (opt_text, immed)) =
   let
     val (finish_text, terminal_pos, finished_pos) =
       (case opt_text of
         NONE => (Method.finish_text (NONE, immed), Position.none, prev_pos)
       | SOME (text, (pos, end_pos)) => (Method.finish_text (SOME text, immed), pos, end_pos));
   in
     Seq.APPEND (fn state =>
       state
       |> assert_forward
       |> assert_bottom bot
       |> close_block
       |> assert_current_goal true
       |> using_facts []
       |> `before_qed |-> (refine o the_default Method.succeed_text)
       |> Seq.maps_results (refine finish_text),
       method_error "terminal" terminal_pos)
     #> Seq.maps_results (Seq.single o finished_goal finished_pos)
   end;
 
 fun check_result msg sq =
   (case Seq.pull sq of
     NONE => error msg
   | SOME (s, _) => s);
 
 
 (* unstructured refinement *)
 
 fun defer i =
   assert_no_chain #>
   refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL defer_tac i)));
 
 fun prefer i =
   assert_no_chain #>
   refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL prefer_tac i)));
 
 fun apply (text, (pos, _)) =
   Seq.APPEND (assert_backward #> refine text #> Seq.map_result (using_facts []),
     method_error "" pos);
 
 fun apply_end (text, (pos, _)) =
   Seq.APPEND (assert_forward #> refine_end text, method_error "" pos);
 
 
 
 (** goals **)
 
 (* generic goals *)
 
 local
 
 val is_var =
   can (dest_TVar o Logic.dest_type o Logic.dest_term) orf
   can (dest_Var o Logic.dest_term);
 
 fun implicit_vars props =
   let
     val var_props = take_prefix is_var props;
     val explicit_vars = fold Term.add_vars var_props [];
     val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);
   in map (Logic.mk_term o Var) vars end;
 
 fun refine_terms n =
   refine_singleton (Method.Basic (fn ctxt => CONTEXT_TACTIC o
     K (HEADGOAL (PRECISE_CONJUNCTS n
       (HEADGOAL (CONJUNCTS (ALLGOALS (resolve_tac ctxt [Drule.termI]))))))));
 
 in
 
 fun generic_goal kind before_qed after_qed goal_ctxt goal_propss result_binds state =
   let
     val chaining = can assert_chain state;
     val pos = Position.thread_data ();
 
     val goal_props = flat goal_propss;
     val vars = implicit_vars goal_props;
     val propss' = vars :: goal_propss;
     val goal_propss = filter_out null propss';
 
     val goal =
       Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss)
       |> Thm.cterm_of goal_ctxt
       |> Thm.weaken_sorts' goal_ctxt;
     val statement = ((kind, pos), propss', Thm.term_of goal);
 
     val after_qed' = after_qed |>> (fn after_local => fn results =>
       map_context (fold Variable.maybe_bind_term result_binds) #> after_local results);
   in
     state
     |> assert_forward_or_chain
     |> enter_forward
     |> open_block
     |> enter_backward
     |> map_context
       (K goal_ctxt
         #> init_context
         #> Variable.set_body true
         #> Proof_Context.auto_bind_goal goal_props)
     |> set_goal (make_goal (statement, [], Goal.init goal, before_qed, after_qed'))
     |> chaining ? (`the_facts #-> using_facts)
     |> reset_facts
     |> not (null vars) ? refine_terms (length goal_propss)
     |> null goal_props ? refine_singleton (Method.Basic Method.assumption)
   end;
 
 fun generic_qed state =
   let
     val (goal_ctxt, {statement = (_, propss, _), goal, after_qed, ...}) =
       current_goal state;
     val results = tl (conclude_goal goal_ctxt goal propss);
   in state |> close_block |> pair (after_qed, (goal_ctxt, results)) end;
 
 end;
 
 
 (* local goals *)
 
 fun local_goal print_results prep_statement prep_att strict_asm
     kind before_qed after_qed raw_fixes raw_assumes raw_shows state =
   let
     val ctxt = context_of state;
 
     val add_assumes =
       Assumption.add_assms
         (if strict_asm then Assumption.assume_export else Assumption.presume_export);
 
     (*params*)
     val ({fixes = params, assumes = assumes_propss, shows = shows_propss,
           result_binds, result_text, text}, params_ctxt) = ctxt
       |> prep_statement raw_fixes (map snd raw_assumes) (map snd raw_shows);
 
     (*prems*)
     val (assumes_bindings, shows_bindings) =
       apply2 (map (apsnd (map (prep_att ctxt)) o fst)) (raw_assumes, raw_shows);
     val (that_fact, goal_ctxt) = params_ctxt
       |> fold Proof_Context.augment (text :: flat (assumes_propss @ shows_propss))
       |> fold_burrow add_assumes ((map o map) (Thm.cterm_of params_ctxt) assumes_propss)
       |> (fn (premss, ctxt') =>
           let
             val prems = Assumption.local_prems_of ctxt' ctxt;
             val ctxt'' =
               ctxt'
               |> not (null assumes_propss) ?
                 (snd o Proof_Context.note_thms ""
                   ((Binding.name Auto_Bind.thatN, []), [(prems, [])]))
               |> (snd o Proof_Context.note_thmss ""
                   (assumes_bindings ~~ map (map (fn th => ([th], []))) premss))
           in (prems, ctxt'') end);
 
     (*result*)
     val results_bindings = map (apfst Binding.default_pos) shows_bindings;
     fun after_qed' (result_ctxt, results) state' =
       let
         val ctxt' = context_of state';
         val export0 =
           Assumption.export false result_ctxt (Proof_Context.augment result_text ctxt') #>
           fold_rev (fn (x, v) => Thm.forall_intr_name (x, Thm.cterm_of params_ctxt v)) params #>
           Raw_Simplifier.norm_hhf_protect ctxt';
         val export = map export0 #> Variable.export result_ctxt ctxt';
       in
         state'
         |> map_context (Proof_Context.augment result_text)
         |> local_results (results_bindings ~~ burrow export results)
         |-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
         |> after_qed (result_ctxt, results)
       end;
   in
     state
     |> generic_goal kind before_qed (after_qed', K I) goal_ctxt shows_propss result_binds
     |> pair that_fact
   end;
 
 fun local_qeds arg =
   end_proof false arg
   #> Seq.map_result (generic_qed #-> (fn ((after_qed, _), results) => after_qed results));
 
 fun local_qed arg =
   local_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
 
 
 (* global goals *)
 
 fun global_goal prep_propp before_qed after_qed propp ctxt =
   let
     val (propss, binds) =
       prep_propp (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) propp;
     val goal_ctxt = ctxt
       |> (fold o fold) Proof_Context.augment propss
       |> fold Variable.bind_term binds;
     fun after_qed' (result_ctxt, results) ctxt' = ctxt'
       |> Proof_Context.restore_naming ctxt
       |> after_qed (burrow (Proof_Context.export result_ctxt ctxt') results);
   in
     ctxt
     |> init
     |> generic_goal "" before_qed (K I, after_qed') goal_ctxt propss []
   end;
 
 val theorem = global_goal Proof_Context.cert_propp;
 val theorem_cmd = global_goal Proof_Context.read_propp;
 
 fun global_qeds arg =
   end_proof true arg
   #> Seq.map_result (generic_qed #> (fn (((_, after_qed), results), state) =>
     after_qed results (context_of state)));
 
 fun global_qed arg =
   global_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
 
 
 (* relevant proof states *)
 
 fun schematic_goal state =
   let val (_, {statement = (_, _, prop), ...}) = find_goal state
   in Goal.is_schematic prop end;
 
 fun is_relevant state =
   (case try find_goal state of
     NONE => true
   | SOME (_, {statement = (_, _, prop), goal, ...}) =>
       Goal.is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
 
 
 (* terminal proof steps *)
 
 local
 
 fun terminal_proof qeds initial terminal state =
   let
     val ctxt = context_of state;
     val check_closure = Method.check_text ctxt #> Method.map_source (Method.method_closure ctxt);
     val initial' = apfst check_closure initial;
     val terminal' = (apfst o Option.map o apfst) check_closure terminal;
   in
     if Goal.skip_proofs_enabled () andalso not (is_relevant state) then
       state
       |> proof (SOME (Method.sorry_text true, #2 initial'))
       |> Seq.maps_results (qeds (#2 (#2 initial), (NONE, #2 terminal)))
     else
       state
       |> proof (SOME initial')
       |> Seq.maps_results (qeds (#2 (#2 initial), terminal'))
   end |> Seq.the_result "";
 
 in
 
 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
 val local_default_proof = local_terminal_proof ((Method.standard_text, Position.no_range), NONE);
 val local_immediate_proof = local_terminal_proof ((Method.this_text, Position.no_range), NONE);
 val local_done_proof = terminal_proof local_qeds (Method.done_text, Position.no_range) (NONE, false);
 
 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
 val global_default_proof = global_terminal_proof ((Method.standard_text, Position.no_range), NONE);
 val global_immediate_proof = global_terminal_proof ((Method.this_text, Position.no_range), NONE);
 val global_done_proof = terminal_proof global_qeds (Method.done_text, Position.no_range) (NONE, false);
 
 end;
 
 
 (* skip proofs *)
 
 fun local_skip_proof int state =
   local_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
   Skip_Proof.report (context_of state);
 
 fun global_skip_proof int state =
   global_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
   Skip_Proof.report (context_of state);
 
 
 (* common goal statements *)
 
 fun internal_goal print_results mode =
   local_goal print_results
     (fn a => fn b => fn c => Proof_Context.cert_statement a b c o Proof_Context.set_mode mode) (K I);
 
 local
 
 fun gen_have prep_statement prep_att strict_asm before_qed after_qed fixes assumes shows int =
   local_goal (Proof_Display.print_results int (Position.thread_data ()))
     prep_statement prep_att strict_asm "have" before_qed after_qed fixes assumes shows;
 
 fun gen_show prep_statement prep_att strict_asm before_qed after_qed fixes assumes shows int state =
   let
     val testing = Unsynchronized.ref false;
     val rule = Unsynchronized.ref (NONE: thm option);
     fun fail_msg ctxt =
       "Local statement fails to refine any pending goal" ::
       (case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
       |> cat_lines;
 
     val pos = Position.thread_data ();
     fun print_results ctxt res =
       if ! testing then ()
       else Proof_Display.print_results int pos ctxt res;
     fun print_rule ctxt th =
       if ! testing then rule := SOME th
       else if int then
         Proof_Display.string_of_rule ctxt "Successful" th
         |> Markup.markup Markup.text_fold
         |> Output.state
       else ();
     val test_proof =
       local_skip_proof true
       |> Unsynchronized.setmp testing true
       |> Exn.interruptible_capture;
 
     fun after_qed' (result_ctxt, results) state' = state'
       |> refine_goals print_rule result_ctxt (flat results)
       |> check_result "Failed to refine any pending goal"
       |> after_qed (result_ctxt, results);
   in
     state
     |> local_goal print_results prep_statement prep_att strict_asm
       "show" before_qed after_qed' fixes assumes shows
     ||> int ? (fn goal_state =>
       (case test_proof (map_context (Context_Position.set_visible false) goal_state) of
         Exn.Res _ => goal_state
       | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
   end;
 
 in
 
 val have = gen_have Proof_Context.cert_statement (K I);
 val have_cmd = gen_have Proof_Context.read_statement Attrib.attribute_cmd;
 val show = gen_show Proof_Context.cert_statement (K I);
 val show_cmd = gen_show Proof_Context.read_statement Attrib.attribute_cmd;
 
 end;
 
 
 
 (** future proofs **)
 
 (* full proofs *)
 
 local
 
 structure Result = Proof_Data
 (
   type T = thm option;
   fun init _ = NONE;
 );
 
 fun the_result ctxt =
   (case Result.get ctxt of
     NONE => error "No result of forked proof"
   | SOME th => th);
 
 val set_result = Result.put o SOME;
 val reset_result = Result.put NONE;
 
 in
 
 fun future_proof fork_proof state =
   let
     val _ = assert_backward state;
     val (goal_ctxt, goal_info) = find_goal state;
     val {statement as (kind, _, prop), using, goal, before_qed, after_qed} = goal_info;
 
     val _ = is_relevant state andalso error "Cannot fork relevant proof";
 
     val after_qed' =
       (fn (_, [[th]]) => map_context (set_result th),
        fn (_, [[th]]) => set_result th);
     val result_ctxt =
       state
       |> map_context reset_result
       |> map_goal (K (goal_ctxt, (kind, [[], [prop]], prop), using, goal, before_qed, after_qed'))
       |> fork_proof;
 
     val future_thm = Future.map (the_result o snd) result_ctxt;
     val finished_goal = Goal.protect 0 (Goal.future_result goal_ctxt future_thm prop);
     val state' =
       state
       |> map_goal (K (goal_ctxt, statement, using, finished_goal, NONE, after_qed));
   in (Future.map fst result_ctxt, state') end;
 
 end;
 
 
 (* terminal proofs *)  (* FIXME avoid toplevel imitation -- include in PIDE/document *)
 
 local
 
 fun future_terminal_proof proof1 proof2 done state =
   if Future.proofs_enabled 3 andalso
     not (Proofterm.proofs_enabled ()) andalso
     not (is_relevant state)
   then
     state |> future_proof (fn state' =>
       let val pos = Position.thread_data () in
         Execution.fork {name = "Proof.future_terminal_proof", pos = pos, pri = ~1}
           (fn () => ((), Timing.protocol "by" pos proof2 state'))
       end) |> snd |> done
   else proof1 state;
 
 in
 
 fun local_future_terminal_proof meths =
   future_terminal_proof
     (local_terminal_proof meths)
     (local_terminal_proof meths #> context_of) local_done_proof;
 
 fun global_future_terminal_proof meths =
   future_terminal_proof
     (global_terminal_proof meths)
     (global_terminal_proof meths) global_done_proof;
 
 end;
 
 end;
diff --git a/src/Tools/try.ML b/src/Tools/try.ML
--- a/src/Tools/try.ML
+++ b/src/Tools/try.ML
@@ -1,108 +1,105 @@
 (*  Title:      Tools/try.ML
     Author:     Jasmin Blanchette, TU Muenchen
     Author:     Makarius
 
 Manager for tools that should be tried on conjectures.
 *)
 
 signature TRY =
 sig
   val serial_commas: string -> string list -> string list
-  val subgoal_count: Proof.state -> int
   type body = bool -> Proof.state -> bool * (string * string list)
   type tool = {name: string, weight: int, auto_option: string, body: body}
   val get_tools: theory -> tool list
   val try_tools: Proof.state -> (string * string) option
   val tool_setup: tool -> unit
 end;
 
 structure Try : TRY =
 struct
 
 (* helpers *)
 
 fun serial_commas _ [] = ["??"]
   | serial_commas _ [s] = [s]
   | serial_commas conj [s1, s2] = [s1, conj, s2]
   | serial_commas conj [s1, s2, s3] = [s1 ^ ",", s2 ^ ",", conj, s3]
   | serial_commas conj (s :: ss) = s ^ "," :: serial_commas conj ss;
 
-val subgoal_count = Logic.count_prems o Thm.prop_of o #goal o Proof.goal;
-
 
 (* configuration *)
 
 type body = bool -> Proof.state -> bool * (string * string list);
 type tool = {name: string, weight: int, auto_option: string, body: body};
 
 fun tool_ord (tool1: tool, tool2: tool) =
   prod_ord int_ord string_ord ((#weight tool1, #name tool1), (#weight tool2, #name tool2));
 
 structure Data = Theory_Data
 (
   type T = tool list;
   val empty = [];
   val extend = I;
   fun merge data : T = Ord_List.merge tool_ord data;
 );
 
 val get_tools = Data.get;
 
 val register_tool = Data.map o Ord_List.insert tool_ord;
 
 
 (* try command *)
 
 fun try_tools state =
-  if subgoal_count state = 0 then
+  if Proof.goal_finished state then
     (writeln "No subgoal!"; NONE)
   else
     get_tools (Proof.theory_of state)
     |> tap (fn tools =>
                "Trying " ^ space_implode " "
                     (serial_commas "and" (map (quote o #name) tools)) ^ "..."
                |> writeln)
     |> Par_List.get_some
            (fn {name, body, ...} =>
                case try (body false) state of
                  SOME (true, (outcome_code, _)) => SOME (name, outcome_code)
                | _ => NONE)
     |> tap (fn NONE => writeln "Tried in vain" | _ => ());
 
 val _ =
   Outer_Syntax.command \<^command_keyword>\<open>try\<close>
     "try a combination of automatic proving and disproving tools"
     (Scan.succeed (Toplevel.keep_proof (ignore o try_tools o Toplevel.proof_of)));
 
 
 (* asynchronous print function *)
 
 fun print_function ({name, weight, auto_option, body}: tool) =
   Command.print_function ("auto_" ^ name)
     (fn {keywords, command_name, ...} =>
       if Keyword.is_theory_goal keywords command_name andalso Options.default_bool auto_option then
         SOME
          {delay = SOME (seconds (Options.default_real \<^system_option>\<open>auto_time_start\<close>)),
           pri = ~ weight,
           persistent = true,
           strict = true,
           print_fn = fn _ => fn st =>
             let
               val state = Toplevel.proof_of st
                 |> Proof.map_context (Context_Position.set_visible false)
               val auto_time_limit = Options.default_real \<^system_option>\<open>auto_time_limit\<close>
             in
               if auto_time_limit > 0.0 then
                 (case Timeout.apply (seconds auto_time_limit) (fn () => body true state) () of
                   (true, (_, outcome)) => List.app Output.information outcome
                 | _ => ())
               else ()
             end handle exn => if Exn.is_interrupt exn then Exn.reraise exn else ()}
       else NONE);
 
 
 (* tool setup *)
 
 fun tool_setup tool = (Theory.setup (register_tool tool); print_function tool);
 
 end;